Tools › Mechanical Design › Brakes, Clutches and Belts

Brakes, Clutches and Belts

Belt, Clutch and Brake Torque

Torque, tensions and actuating forces of the classical friction drives and brakes, three analyses under one select. Belt drive: open or crossed flat or V belt between two pulleys, wrap angles and belt length (exact and series forms), belt speed, centrifugal tension, Euler's tension ratio with the groove-angle correction, the tensions and the initial tension that just carry the entered power or torque, or the slip limit of an entered initial tension, belt stresses with the bending term, and a chart of the tensions against power. Disc or cone clutch: actuating force and torque capacity by the uniform-wear and uniform-pressure assumptions side by side, the force and pressure for a required torque, the optimum inner radius. Drum or band brake: short-shoe and long-shoe internal or external shoes with the moments of the normal and friction forces about the hinge pin written out, the actuating force, the self-energizing and self-locking checks and the hinge-pin reaction; simple and differential band brakes with the lever force; and the energy, time and mean power of a stop from the inertia with the temperature rise of the drum. Closed forms of classical mechanics checked by an independent numpy/scipy integration; the default cases are illustrative (V belt 2β 38°, 6 and 12 in pulleys, 1,750 rpm, 5 hp; disc clutch 4 and 6 in radii at 100 lb/in²; 10 in internal drum with a 90° shoe at 150 lb/in²) and the Navy Basic Machines Prony-brake example is reproduced by the test.

1 worked example reproduced, listed on the tool page.

Keys, Splines and Couplings

Strength and sizing of the shaft-to-hub connections of a drive, seven analyses under one select. Parallel, taper and feather keys: the standard key size for the shaft from the Navy and Army machinist tables (the ANSI series as printed there), key shear 2T/(d w L) and crushing 4T/(d h L) on the hub and shaft sides, the length that an entered allowable needs, the keyseat depth and the bottom-of-keyway dimension, the keyseat fatigue factors of NASA RP-1123 (profiled or sled-runner, annealed or hardened), the 0.75 rule for the torque a keyseated shaft can carry, the 1/8 in per foot taper and the sliding force of a feather key. Woodruff keys by their number with the Army table of keyway depths and the segment geometry. Involute splines: pitch, base, major and minor diameters from the tooth count and pressure angle, the bearing, tooth-shear and torsional stresses of the Army helicopter handbooks with the contact fraction, the allowable bearing stresses of their Table 7-4, the sliding force and the bursting stress of the internal member. SAE straight-sided splines (4, 6, 10, 16) from the proportions printed in TC 9-524. Bolted flange couplings: bolt shear and bearing from the service-factor torque, the friction grip from the bolt preload, the flange shear at the hub and the key in each hub; the reaction moment and forces of a misaligned flexible coupling from its catalogue stiffnesses. Cross pins in double shear with the bearing in shaft and hub, set screws by their holding power, and the torsional stiffness of the whole assembly as springs in series. Every closed form is checked by an independent numpy/scipy script; the default cases are illustrative (a 2 in shaft with a 1/2 in square key under 3,000 lb-in) except the involute spline, which is the NASA-tested SSME preburner spline.

1 worked example reproduced, listed on the tool page.

Other Mechanical Design sections

Shafts · Gears · Bearings · Springs · Fasteners and Power Screws · Pressure Vessels · Tolerances · Mass Properties · Vibration · Acoustics · Machining and Manufacturing · Lubrication and Wear